Pressure of 1 mol of an ideal gas confined in a cylinder fitted with a piston is 50 atm. The gas is expanded reversible when the cylinder is kept in contact to a thermostat at `25^(@)C`. During expansion, the pressure of the gas is decreased from 50 to 5 atm. calculate the change in entropy in this process. if the heat absorbed by the gas during expansion be 5705J, then calculate the change in entropy of the surroundings ?

Explanation

We know, `DeltaS=2.303nR" log"(P_(1))/(P_(2))`
Given, `P_(1)=50atm, P_(2)=5atm and n=1`
`therefore` The change in entropy of the system (i.e., gas),
`DeltaS=2.303xx8.314" log"(50)/(5)=19.15J*K^(-1)`
Here surrounding is at a fixed temperature `(25^(@)C)`. during expansion, the heat absorbed by the gas from the surroundings=5705 J. therefore, at `25^(@)C`, heat released by the surroundings=-5705 J
`therefore`Change entropy of the surroudings,
`DeltaS_("surr")=-(5705)/((273+25))J*K^(-1)=-19.14J*K^(-1)`.